Detroit. Willesden. Olympos, on the Greek island of Karpathos. “The inside of our skulls”. These are the places that make up Holy Fire, Foals third album, their most direct and fully realised album yet. Foals have stepped up from, as Yannis puts it, "songs for indie clubs" to something much, much bigger. Their third album might not sound like Depeche Mode or Nine Inch Nails, but it has much of the same ambitious spirit and grandiose aesthetic that led to those groups touching the lives of millions. This is the sound of Foals arriving.

It's all a long way from the group's early years in Oxford, where Yannis Philippakis (26), Jack Bevan (27), Walter Gervers (28), Edwin Congreave (28) and Jimmy Smith (28) convened after spells in various well regarded bands such as The Edmund Fitzgerald, whose intricacies were a league away from the Libertines-influenced indie skiffle and American garage rock that dominated at the time. Debut album Antidotes (2008) attempted to capture the live energy and sense of spontaneity that had made Foals one of the most sought-after live acts in the UK. 2010 follow-up Total Life Forever was a surprise to many (Foals never sit still for long) dealing in more expansive, eloquent sounds and a more mellow feel inspired in part by Foals' long-time enthusiasm for weed. Now, as they approach their 30s, Foals are moving on from the "kind of lost boys club element to how we've lived for the past six years" to make their best music yet.

Yannis gives much of the credit for this huge leap forward to producers Flood and Alan Moulder. "The two of them have a knack of taking something that at its core is fairly leftfield or fairly idiosyncratic, and whatever they capture becomes a universal experience," he says. "I'd be lying if I said it wasn't something that attracted us to them.

The feeling is mutual. Alan Moulder, who mixed Total Life Forever, says “I was impressed with their attitude to making a record and their ambition towards achieving something individual and unique but still wanting to appeal to the "masses".

During the recording sessions at Flood and Moulder’s Assault & Battery studios in Willesden, North West London, the producers encouraged the band to create the right atmosphere in the room. “One of our aims was to capture the feel of the band playing live and to be able to easily experiment,” says Flood, “so we all helped to create an environment that the band felt was creative but also somewhere you could be 12 hours a day.”

"The band couldn't draw on the external way that it could in the way that it did when it went to Sweden or New York, which were new experiences," Yannis explains. "Whether it was inside our own skulls or in the studio we formed our own worlds, and one way of doing that was to bring in vegetation. It was all quite tropical vegetation. It enhanced the feeling of the pestilence and the swamps on the tracks where it needed to feel sweaty and marshy."

This all became part of the influences that went into Holy Fire, described by Yannis as "The Delta, voodoo, the swamp, sexuality, byzantine iconography and music, syrupy rhythms, the mountains, the abyss, the decline of the bee populations, hip hop and stoner rock." Then there's the folk music of the American Deep South, captured by Alan Lomax just before it passed into history: “most of the players of the music are long deceased, but you can still be part of these moments that were recorded in fields in the Delta," says Yannis. "You feel like there's a direct communion happening between you and a ghost."

To capture this directness from Foals themselves, Flood and Moulder deployed the devious tactic of letting the band think they were running through demos of tracks, when in fact actual takes were being recorded. “Sometimes early takes have an edge to them,” Moulder explains. “The band aren't over-thinking as they aren't aware they are being recorded and sometimes you get some gems; and we did!”

"It's pure expression, from the emotion, into the instrument, into the microphone, out of the microphone, into the speaker and then to the listener - it feels like raising the dead for three minutes." Yannis says. "There's something that's exciting for us to feel that every time you put on the record, you commune with something that's in the past."

This approach was an unqualified success. You can hear it on the astonishing, almost bombastic 'Inhaler', the first track to be released from Holy Fire. "It's heavy, that song; it was liberating," says Yannis, adding that it is the sound of the band shedding their inhibitions. "Those songs have always been in us the whole time, and there's always been a self-censorship that's been prior to this. One thing that was liberating was to feel that we could do whatever we want, there could be a radical freedom to it, but it still ends up sound like we do. We could express a new range of emotions, rage or claustrophobia. There's less head going on and more heart."

Yet this is never at the expense of Foals losing the love of rhythm and pop melodies that made them who they are – that much can be heard in the earworm hook of ‘My Number’, about which Yannis says “it could be a very literal thing in terms of people not having each other's numbers and being unable to communicate, then on a broader sense being part of a community where you're misunderstood. I like the cocksurety of the emotion, the flippant nature of it.”

Yannis feels that Holy Fire features his strongest lyricism to date. "The lyrics for the first album were like a kiss chase with no payoff," he says. "It was just abstractions. There was genuine emotion behind it but I wasn't willing to verbalise it." Now, though with a philosophy of refusing to self censor, it's all there, for everyone. "There might be some utility in that for a 15-year-old who's going to listen to it and get solace from it," Yannis says. Foals have not made a record for those who might think that it is "going to look great with their latte and their loafers. I want to make songs for people who I feel like have been disenfranchised by alternative rock music".

Take 'Late Night', for instance. “Some of that is to do with my grandmother, and to do with ageing, and being on the verge of passing over into something else, and having remorse and guilt." Catholic guilt? "Byzantine guilt… bloodlines, and disappointment, and the unwinding of genes."

Much like the classic Depeche Mode, Nine Inch Nails and Smashing Pumpkins albums that Flood and Moulder have previously collaborated on, Holy Fire finds Foals uniting the personal with bigger themes – specifically feelings of contemporary dread. So album closer ‘Moon’ is one of the most affecting pieces the band have written, “describing the end of the world, the destruction of your body and everything disintegrating,” Yannis says. “It's acceptance, a beautiful type of destruction, you're in a pacific state with no resentment or sorrow.”

This developed from an experience on Foals’ last tour of the US. “We went to Detroit and it affected me like no other place has before,” Yannis says. “I saw these blue collar workers who you could imagine 15 years ago working as these honest Americans, but everything had obviously been collapsed in by crystal meth. Opposite the venue were these tenement blocks where most of the windows were smashed out and there'd be lights flickering inside, and it was just freakish, it was dystopian. It was the embodiment of the fall of the Empire.”

Yet in contrast to this observed hell is Yannis’ own personal place of solace. Halfway through the recording of Holy Fire, Yannis felt the need to retreat to Olympos, the remote village in Greece that is his family’s home. “I was getting a bit lost being in Willesden and the studio the whole time, whirlwinding a little bit,” Yannis says. In Greece, he says, “I've got a duel identity. I start to get lost and tie myself in knots when I've been here too long, and I forget that there's this whole other thing that I can plug into and it feels like this archaic backbone that's I'm part of.” There, where his father still makes traditional musical instruments and "creative values are paramount", people participate in songs, sagas and dances that date back hundreds of years to the Byzantine Empire. “It's very evocative of this long gone time,” Yannis says. ”Plugging in makes me feel connected to this bloodline. It makes me sturdy again.”

So Holy Fire is a record of contrasts, of Foals feeling themselves liberated to create a record that perhaps they didn’t even realise they had within them. "It's been the least harrowing of all the records,” says Yannis, before adding, ”in a lot of ways it's not been harrowing at all, and I think a lot of that has been Flood and Moulder. We vacillate between our experimental side and the side that enjoys the possibilities of what pop music can do, that it can speak outside it's own barrier. If anything we feel that we've made a record that doesn't exist between those two subsets. I feel content that we've made a record that is just what it should have been.”